Efficient implementation of filters for mimo fading

ABSTRACT

A single finite impulse response filter designed to operate on a single signal is used in conjunction with an input multiplexer that interleaves samples from multiple signals and an output decimator. The output of the decimator contains interleaved samples of the multiple signals with independent filtering applied to each.

BACKGROUND

Multi-path fading is a contributing factor to microwave radio receivererror rates. Its effects can be reduced by employing transmitters withmultiple outputs and receivers with multiple inputs. Simulating thedynamic multi-path fading behavior of such multi-input, multi-output(MIMO) communication channels is necessary to properly characterize themicrowave radio equipment.

The most general linear model for a MIMO multi-path fader is shown inFIG. 1. Each Filter (m,n) block represents a time varying filter. Anyset of band limited signals can be down converted and sampled so thefiltering may be applied using a discrete time digital filter operatingon a complex (I/Q) data sequence. Generally, each filter is implementedas an independent Finite Impulse Response (FIR) filter with time-varyingcomplex coefficients (taps). After filtering, the signals can beup-converted and reconstructed as continuous time waveforms.

The key parameters associated with this multi-path fader are: the numberof input and output channels supported, the filter sample rate, thenumber of taps in each filter, the maximum rate at which the filter tapscan be updated, and the precision of the filter math.

SUMMARY

A MIMO multi-path fader can be constructed using a single finite impulseresponse filter designed to operate on a single signal in conjunctionwith an input multiplexer that interleaves samples from multiple signalsand an output decimator. The output of the decimator containsinterleaved samples of the multiple signals with independent filteringapplied to each.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates a functional block diagram of prior art multi-pathfader.

FIG. 2 illustrates a functional block diagram according to the presentinvention.

FIG. 3 illustrates an efficient implementation of a single channelfinite impulse response (FIR) filter by transforming to the frequencydomain, multiplying, and transforming back to the time domain.

DETAILED DESCRIPTION

FIG. 2 illustrates a functional block diagram of a multi-path faderaccording to the present invention. A multi-path fader can beconstructed using a single finite impulse response (FIR) filter designedto operate on a single signal in conjunction with an input multiplexerthat interleaves samples from multiple signals and an output decimator.The output of the decimator (implemented as a demultiplexor) containsinterleaved samples of the multiple signals with independent filteringapplied to each.

The input multiplexer implements the data interleave pattern (shown inTable 1) used to emulate all six filters of a 3-input, 2-output MIMOsystem in a single FIR filter. The top row shows the composite tapsequence where each c_(m,n,k) is the k^(th) tap from filter (m,n). Thesubsequent rows show the corresponding data alignment versus clockcycle, where x_(n,r) is the r^(th) sample of input n. New data enters atthe left and is shifted right one column per clock interval. The rightcolumn shows outputs computed as the inner product of that row with thetaps, where y_(m,r) is the r^(th) sample of output m.

TABLE 1 Interleaved Taps/Data for a 3 × 2 MIMO composite filterc_(0,0,k) c_(1,0,k) c_(0,1,k) c_(1,1,k) c_(0,2,k) c_(1,2,k) c_(0,0,k+1)c_(1,0,k+1) X_(2,r) 0 x_(0,r−1) 0 X_(1,r−1) 0 x_(2,r−1) 0 (none) 0X_(2,r) 0 x_(0,r−1) 0 x_(1,r−1) 0 x_(2,r−1) (none) X_(1,r) 0 x_(2,r) 0X_(0,r−1) 0 x_(1,r−1) 0 (none) 0 X_(1,r) 0 X_(2,r) 0 x_(0,r−1) 0x_(1,r−1) (none) X_(0,r) 0 x_(1,r) 0 X_(2,r) 0 x_(0,r−1) 0 y_(0,r) 0X_(0,r) 0 X_(1,r) 0 x_(2,r) 0 x_(0,r−1) y_(1,r)

The filter tap pattern from Table-1 may be generalized to any number ofinputs, outputs, and taps by using the algebraic representation inEquation 1, where N is the number of inputs, M is the number of outputs,K is the number of taps in each filter. The c_(i)′ values are the tapsof the composite filter with interleaved coefficients, where 0≦i<KNM.

c _(i) ′=c _(m,n,k) ,i=kNM+nM+m,0≦n<N,0≦m<M,0≦k<K  Equation (1)

The input sequence, x_(j)′, for the generalized composite filter isderived from the N individual input sequences as shown in equation-2,where x_(n,r) is the r^(th) sample of input n.

$\begin{matrix}{x_{j}^{\prime} = \left\{ \begin{matrix}{x_{{N - 1 - {{({j\mspace{14mu} {mod}\mspace{14mu} {NM}})}/M}},{{Floor}{({j/{NM}})}}},} & {{{when}\mspace{14mu} j\mspace{14mu} {mod}\mspace{14mu} M} = 0} \\0 & {otherwise}\end{matrix} \right.} & {{Equation}\mspace{14mu} (2)}\end{matrix}$

The output decimator extracts the individual multiple sample outputsfrom the composite filter output sequence y_(p)′ using Equation 3, wherey_(m,r) is the r^(th) sample of output m. All outputs failing the statedcondition are discarded.

y _(p mod MN,Floor(p/MN)) =y _(p) ′,pmodMN<M  Equation (3)

The relative alignment of the composite input index, j, in Equation 2and the output index, p, in Equation 3 must be appropriately defined.This is accomplished by assigning the p=0 index to the inner productcomputed when the j=M(N−1) input sample (i.e. x_(0,0)) is aligned withthe first composite filter tap (i=0).

From the preceding formulas, the single composite filter must have Mtimes N as many taps as the individual filters, and its computationalrate is increased by the same factor. This is an acceptable tradeoffwhen a single, high-speed, long tap-count filter is more efficientlyimplemented than multiple smaller filters. At this point, digital signalprocessing techniques, such as that disclosed by Oppenheim and Schaferin “Discrete-Time Signal Processing,” Prentice Hall, 1989, Section 8.9,Linear Convolution Using the Discrete Fourier Transform, pp 548-561, canbe applied to the signal to improve computational efficiency. Toillustrate, the real or complex filter coefficients may be transformedfrom the time domain to the frequency domain via a Fast FourierTransform (FFT), multiplied, and then transformed from the frequencydomain to the time domain via an inverse FFT (as shown in FIG. 3).

1. A circuit comprising: an input multiplexer that interleaves samplesfrom multiple signals, having a multiplexed signal; a single finiteimpulse response filter designed to operate on a single signal, having afilter output, receiving the multiplexed signal as an input signal; anda decimator/demultiplexer, receiving the filter output, having multipleoutput signals, wherein the multiple output signals contain samples ofthe multiple signals with independent filtering applied to each.
 2. Acircuit, as in claim 1, the single finite impulse response filterincluding: performing sequentially, transforming blocks of the inputsignal from the time domain into the frequency domain; multiplying byfrequency domain coefficients; and transforming from the frequencydomain to the time domain.
 3. A circuit, as in claim 2, wherein eachblock of the input signal is multiplied by a unique set of frequencydomain coefficients.
 4. A circuit, as in claim 2, wherein the frequencydomain coefficients are Fourier transforms of interleaved time domaincoefficients.
 5. A circuit as in claim 1 wherein the time domain filtercoefficients are complex.